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<div class="header">
  <div class="summary">
<a href="#enum-members">Enumerations</a> &#124;
<a href="#func-members">Functions</a> &#124;
<a href="#var-members">Variables</a>  </div>
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Enumerations</h2></td></tr>
<tr class="memitem:a02c20a1b1d35988c657aa1e219d609d5"><td class="memItemLeft" align="right" valign="top">enum &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5">CoordinateAxis</a> { <a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">CoordinateAxis::X</a>, 
<a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a57cec4137b614c87cb4e24a3d003a3e0">CoordinateAxis::Y</a>, 
<a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a21c2e59531c8710156d34a3c30ac81d5">CoordinateAxis::Z</a>
 }</td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:ab66b0f13a5bbe6887c815cc1f97b6a13"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:ab66b0f13a5bbe6887c815cc1f97b6a13"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/d9b/namespaceori.html#ab66b0f13a5bbe6887c815cc1f97b6a13">rad2deg</a> (T rad)</td></tr>
<tr class="separator:ab66b0f13a5bbe6887c815cc1f97b6a13"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:abb3365c40bad692ba94734339d8c9df9"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:abb3365c40bad692ba94734339d8c9df9"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/d9b/namespaceori.html#abb3365c40bad692ba94734339d8c9df9">deg2rad</a> (T deg)</td></tr>
<tr class="separator:abb3365c40bad692ba94734339d8c9df9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a537b8d0769c03e4cd8ef2b9a9dc8a760"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a537b8d0769c03e4cd8ef2b9a9dc8a760"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3</a>&lt; T &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/d9b/namespaceori.html#a537b8d0769c03e4cd8ef2b9a9dc8a760">coordinateRotation</a> (<a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5">CoordinateAxis</a> axis, T theta)</td></tr>
<tr class="separator:a537b8d0769c03e4cd8ef2b9a9dc8a760"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:add867f41c8046a8bba05611e25c8dfcd"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:add867f41c8046a8bba05611e25c8dfcd"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3</a>&lt; typename T::Scalar &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/d9b/namespaceori.html#add867f41c8046a8bba05611e25c8dfcd">rpyToRotMat</a> (const Eigen::MatrixBase&lt; T &gt; &amp;v)</td></tr>
<tr class="separator:add867f41c8046a8bba05611e25c8dfcd"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a153f2a76610f0c5524da3f8bf8fa4dfa"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a153f2a76610f0c5524da3f8bf8fa4dfa"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3</a>&lt; typename T::Scalar &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/d9b/namespaceori.html#a153f2a76610f0c5524da3f8bf8fa4dfa">vectorToSkewMat</a> (const Eigen::MatrixBase&lt; T &gt; &amp;v)</td></tr>
<tr class="separator:a153f2a76610f0c5524da3f8bf8fa4dfa"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0d9277fde185aecf3eae4a6d6450d25f"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a0d9277fde185aecf3eae4a6d6450d25f"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a>&lt; typename T::Scalar &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/d9b/namespaceori.html#a0d9277fde185aecf3eae4a6d6450d25f">matToSkewVec</a> (const Eigen::MatrixBase&lt; T &gt; &amp;m)</td></tr>
<tr class="separator:a0d9277fde185aecf3eae4a6d6450d25f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a73c3872af6870d856cedd662856fcaea"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a73c3872af6870d856cedd662856fcaea"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a>&lt; typename T::Scalar &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/d9b/namespaceori.html#a73c3872af6870d856cedd662856fcaea">rotationMatrixToQuaternion</a> (const Eigen::MatrixBase&lt; T &gt; &amp;r1)</td></tr>
<tr class="separator:a73c3872af6870d856cedd662856fcaea"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af88fa91d686c646d41f9b747a6bc90f0"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:af88fa91d686c646d41f9b747a6bc90f0"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3</a>&lt; typename T::Scalar &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/d9b/namespaceori.html#af88fa91d686c646d41f9b747a6bc90f0">quaternionToRotationMatrix</a> (const Eigen::MatrixBase&lt; T &gt; &amp;q)</td></tr>
<tr class="separator:af88fa91d686c646d41f9b747a6bc90f0"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:add76bed815809cbebd38a8596b0f6224"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:add76bed815809cbebd38a8596b0f6224"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a>&lt; typename T::Scalar &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/d9b/namespaceori.html#add76bed815809cbebd38a8596b0f6224">quatToRPY</a> (const Eigen::MatrixBase&lt; T &gt; &amp;q)</td></tr>
<tr class="separator:add76bed815809cbebd38a8596b0f6224"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ade40aba34aa5e6b4f82753eb3c63d16a"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:ade40aba34aa5e6b4f82753eb3c63d16a"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a>&lt; typename T::Scalar &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/d9b/namespaceori.html#ade40aba34aa5e6b4f82753eb3c63d16a">rpyToQuat</a> (const Eigen::MatrixBase&lt; T &gt; &amp;rpy)</td></tr>
<tr class="separator:ade40aba34aa5e6b4f82753eb3c63d16a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a90e9fca31a184b48790b43aa6f44fcbd"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a90e9fca31a184b48790b43aa6f44fcbd"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a>&lt; typename T::Scalar &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/d9b/namespaceori.html#a90e9fca31a184b48790b43aa6f44fcbd">quatToso3</a> (const Eigen::MatrixBase&lt; T &gt; &amp;q)</td></tr>
<tr class="separator:a90e9fca31a184b48790b43aa6f44fcbd"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a4a1bdfe61995fc50713a5bba4ccbc8cb"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a4a1bdfe61995fc50713a5bba4ccbc8cb"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a>&lt; typename T::Scalar &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/d9b/namespaceori.html#a4a1bdfe61995fc50713a5bba4ccbc8cb">rotationMatrixToRPY</a> (const Eigen::MatrixBase&lt; T &gt; &amp;R)</td></tr>
<tr class="separator:a4a1bdfe61995fc50713a5bba4ccbc8cb"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:afa58699364d5378139e91ec6f0972475"><td class="memTemplParams" colspan="2">template&lt;typename T , typename T2 &gt; </td></tr>
<tr class="memitem:afa58699364d5378139e91ec6f0972475"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a>&lt; typename T::Scalar &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/d9b/namespaceori.html#afa58699364d5378139e91ec6f0972475">quatDerivative</a> (const Eigen::MatrixBase&lt; T &gt; &amp;q, const Eigen::MatrixBase&lt; T2 &gt; &amp;omega)</td></tr>
<tr class="separator:afa58699364d5378139e91ec6f0972475"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a89494866325446c634184782e56113ff"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a89494866325446c634184782e56113ff"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a>&lt; typename T::Scalar &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/d9b/namespaceori.html#a89494866325446c634184782e56113ff">quatProduct</a> (const Eigen::MatrixBase&lt; T &gt; &amp;q1, const Eigen::MatrixBase&lt; T &gt; &amp;q2)</td></tr>
<tr class="separator:a89494866325446c634184782e56113ff"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ac12ecf143879de178929ecaad1714a6a"><td class="memTemplParams" colspan="2">template&lt;typename T , typename T2 , typename T3 &gt; </td></tr>
<tr class="memitem:ac12ecf143879de178929ecaad1714a6a"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a>&lt; typename T::Scalar &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/d9b/namespaceori.html#ac12ecf143879de178929ecaad1714a6a">integrateQuat</a> (const Eigen::MatrixBase&lt; T &gt; &amp;quat, const Eigen::MatrixBase&lt; T2 &gt; &amp;omega, T3 dt)</td></tr>
<tr class="separator:ac12ecf143879de178929ecaad1714a6a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a24ac869b814e7e46a63c4ee97e3279ea"><td class="memTemplParams" colspan="2">template&lt;typename T , typename T2 , typename T3 &gt; </td></tr>
<tr class="memitem:a24ac869b814e7e46a63c4ee97e3279ea"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a>&lt; typename T::Scalar &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/d9b/namespaceori.html#a24ac869b814e7e46a63c4ee97e3279ea">integrateQuatImplicit</a> (const Eigen::MatrixBase&lt; T &gt; &amp;quat, const Eigen::MatrixBase&lt; T2 &gt; &amp;omega, T3 dt)</td></tr>
<tr class="separator:a24ac869b814e7e46a63c4ee97e3279ea"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a26df2f27ad5ea245384c0e20fb0cb1c2"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a26df2f27ad5ea245384c0e20fb0cb1c2"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/d9b/namespaceori.html#a26df2f27ad5ea245384c0e20fb0cb1c2">quaternionToso3</a> (const <a class="el" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a>&lt; T &gt; quat, <a class="el" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a>&lt; T &gt; &amp;so3)</td></tr>
<tr class="separator:a26df2f27ad5ea245384c0e20fb0cb1c2"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1d645df5c53cbaf41b0a10b46baf8f47"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a1d645df5c53cbaf41b0a10b46baf8f47"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a>&lt; T &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/d9b/namespaceori.html#a1d645df5c53cbaf41b0a10b46baf8f47">so3ToQuat</a> (<a class="el" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a>&lt; T &gt; &amp;so3)</td></tr>
<tr class="separator:a1d645df5c53cbaf41b0a10b46baf8f47"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="var-members"></a>
Variables</h2></td></tr>
<tr class="memitem:a324ebc9ef2225bdf72de8d94408bf047"><td class="memItemLeft" align="right" valign="top">static constexpr double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d9b/namespaceori.html#a324ebc9ef2225bdf72de8d94408bf047">quaternionDerviativeStabilization</a> = 0.1</td></tr>
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</table>
<h2 class="groupheader">Enumeration Type Documentation</h2>
<a class="anchor" id="a02c20a1b1d35988c657aa1e219d609d5"></a>
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          <td class="memname">enum <a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5">ori::CoordinateAxis</a></td>
        </tr>
      </table>
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  <td class="mlabels-right">
<span class="mlabels"><span class="mlabel">strong</span></span>  </td>
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<tr><th colspan="2">Enumerator</th></tr><tr><td class="fieldname"><a class="anchor" id="a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383"></a>X&#160;</td><td class="fielddoc">
</td></tr>
<tr><td class="fieldname"><a class="anchor" id="a02c20a1b1d35988c657aa1e219d609d5a57cec4137b614c87cb4e24a3d003a3e0"></a>Y&#160;</td><td class="fielddoc">
</td></tr>
<tr><td class="fieldname"><a class="anchor" id="a02c20a1b1d35988c657aa1e219d609d5a21c2e59531c8710156d34a3c30ac81d5"></a>Z&#160;</td><td class="fielddoc">
</td></tr>
</table>

<p>Definition at line <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00032">32</a> of file <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html">orientation_tools.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;{ <a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>, <a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a57cec4137b614c87cb4e24a3d003a3e0">Y</a>, <a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a21c2e59531c8710156d34a3c30ac81d5">Z</a> };</div><div class="ttc" id="namespaceori_html_a02c20a1b1d35988c657aa1e219d609d5a21c2e59531c8710156d34a3c30ac81d5"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a21c2e59531c8710156d34a3c30ac81d5">ori::CoordinateAxis::Z</a></div></div>
<div class="ttc" id="namespaceori_html_a02c20a1b1d35988c657aa1e219d609d5a57cec4137b614c87cb4e24a3d003a3e0"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a57cec4137b614c87cb4e24a3d003a3e0">ori::CoordinateAxis::Y</a></div></div>
<div class="ttc" id="namespaceori_html_a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">ori::CoordinateAxis::X</a></div></div>
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<h2 class="groupheader">Function Documentation</h2>
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          <td class="memname"><a class="el" href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3</a>&lt;T&gt; ori::coordinateRotation </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5">CoordinateAxis</a>&#160;</td>
          <td class="paramname"><em>axis</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">T&#160;</td>
          <td class="paramname"><em>theta</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
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<p>Compute rotation matrix for coordinate transformation. Note that coordinateRotation(CoordinateAxis:X, .1) * v will rotate v by -.1 radians - this transforms into a frame rotated by .1 radians!. </p>

<p>Definition at line <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00060">60</a> of file <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html">orientation_tools.h</a>.</p>

<p>References <a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>, <a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a57cec4137b614c87cb4e24a3d003a3e0">Y</a>, and <a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a21c2e59531c8710156d34a3c30ac81d5">Z</a>.</p>
<div class="fragment"><div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;                                                         {</div><div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;  static_assert(std::is_floating_point&lt;T&gt;::value,</div><div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;                <span class="stringliteral">&quot;must use floating point value&quot;</span>);</div><div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;  T s = std::sin(theta);</div><div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;  T c = std::cos(theta);</div><div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;</div><div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3&lt;T&gt;</a> R;</div><div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;</div><div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;  <span class="keywordflow">if</span> (axis == CoordinateAxis::X) {</div><div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;    R &lt;&lt; 1, 0, 0, 0, c, s, 0, -s, c;</div><div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (axis == CoordinateAxis::Y) {</div><div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;    R &lt;&lt; c, 0, -s, 0, 1, 0, s, 0, c;</div><div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (axis == CoordinateAxis::Z) {</div><div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;    R &lt;&lt; c, s, 0, -s, c, 0, 0, 0, 1;</div><div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;  }</div><div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;</div><div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;  <span class="keywordflow">return</span> R;</div><div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_aa8cb424e643d476ea485238dad7c3e18"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 3 &gt; Mat3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00054">cppTypes.h:54</a></div></div>
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          <td class="memname">T ori::deg2rad </td>
          <td>(</td>
          <td class="paramtype">T&#160;</td>
          <td class="paramname"><em>deg</em></td><td>)</td>
          <td></td>
        </tr>
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<p>Convert degrees to radians </p>

<p>Definition at line <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00048">48</a> of file <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html">orientation_tools.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;                 {</div><div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;  static_assert(std::is_floating_point&lt;T&gt;::value,</div><div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;                <span class="stringliteral">&quot;must use floating point value&quot;</span>);</div><div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;  <span class="keywordflow">return</span> deg * T(M_PI) / T(180);</div><div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;}</div></div><!-- fragment -->
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          <td class="memname"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a>&lt;typename T::Scalar&gt; ori::integrateQuat </td>
          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>quat</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T2 &gt; &amp;&#160;</td>
          <td class="paramname"><em>omega</em>, </td>
        </tr>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">T3&#160;</td>
          <td class="paramname"><em>dt</em>&#160;</td>
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          <td>)</td>
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<p>Compute new quaternion given: </p><dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">quat</td><td>The old quaternion </td></tr>
    <tr><td class="paramname">omega</td><td>The angular velocity (IN INERTIAL COORDINATES!) </td></tr>
    <tr><td class="paramname">dt</td><td>The timestep </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd></dd></dl>

<p>Definition at line <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00283">283</a> of file <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html">orientation_tools.h</a>.</p>

<p>References <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00262">quatProduct()</a>.</p>
<div class="fragment"><div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;                                              {</div><div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;  static_assert(T::ColsAtCompileTime == 1 &amp;&amp; T::RowsAtCompileTime == 4,</div><div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;                <span class="stringliteral">&quot;Must have 4x1 quat&quot;</span>);</div><div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;  static_assert(T2::ColsAtCompileTime == 1 &amp;&amp; T2::RowsAtCompileTime == 3,</div><div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;                <span class="stringliteral">&quot;Must have 3x1 omega&quot;</span>);</div><div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> axis;</div><div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;  <span class="keyword">typename</span> T::Scalar ang = omega.norm();</div><div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;  <span class="keywordflow">if</span> (ang &gt; 0) {</div><div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;    axis = omega / ang;</div><div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;  } <span class="keywordflow">else</span> {</div><div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;    axis = <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a>(1, 0, 0);</div><div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;  }</div><div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;</div><div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;  ang *= dt;</div><div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> ee = std::sin(ang / 2) * axis;</div><div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat&lt;typename T::Scalar&gt;</a> quatD(std::cos(ang / 2), ee[0], ee[1], ee[2]);</div><div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;</div><div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat&lt;typename T::Scalar&gt;</a> quatNew = <a class="code" href="../../da/d9b/namespaceori.html#a89494866325446c634184782e56113ff">quatProduct</a>(quatD, quat);</div><div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;  quatNew = quatNew / quatNew.norm();</div><div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;  <span class="keywordflow">return</span> quatNew;</div><div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_a8686862774f7c3186c7920447f4de282"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 4, 1 &gt; Quat</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00058">cppTypes.h:58</a></div></div>
<div class="ttc" id="cpp_types_8h_html_a6f07728c866b15ff0676a9b2ebfd2ba6"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 1 &gt; Vec3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00026">cppTypes.h:26</a></div></div>
<div class="ttc" id="namespaceori_html_a89494866325446c634184782e56113ff"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a89494866325446c634184782e56113ff">ori::quatProduct</a></div><div class="ttdeci">Quat&lt; typename T::Scalar &gt; quatProduct(const Eigen::MatrixBase&lt; T &gt; &amp;q1, const Eigen::MatrixBase&lt; T &gt; &amp;q2)</div><div class="ttdef"><b>Definition:</b> <a href="../../d4/dfb/orientation__tools_8h_source.html#l00262">orientation_tools.h:262</a></div></div>
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template&lt;typename T , typename T2 , typename T3 &gt; </div>
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          <td class="memname"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a>&lt;typename T::Scalar&gt; ori::integrateQuatImplicit </td>
          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>quat</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T2 &gt; &amp;&#160;</td>
          <td class="paramname"><em>omega</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">T3&#160;</td>
          <td class="paramname"><em>dt</em>&#160;</td>
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          <td>)</td>
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<p>Compute new quaternion given: </p><dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">quat</td><td>The old quaternion </td></tr>
    <tr><td class="paramname">omega</td><td>The angular velocity (IN INERTIAL COORDINATES!) </td></tr>
    <tr><td class="paramname">dt</td><td>The timestep </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd></dd></dl>

<p>Definition at line <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00315">315</a> of file <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html">orientation_tools.h</a>.</p>

<p>References <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00262">quatProduct()</a>.</p>
<div class="fragment"><div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;           {</div><div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;  static_assert(T::ColsAtCompileTime == 1 &amp;&amp; T::RowsAtCompileTime == 4,</div><div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;                <span class="stringliteral">&quot;Must have 4x1 quat&quot;</span>);</div><div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;  static_assert(T2::ColsAtCompileTime == 1 &amp;&amp; T2::RowsAtCompileTime == 3,</div><div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;                <span class="stringliteral">&quot;Must have 3x1 omega&quot;</span>);</div><div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> axis;</div><div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;  <span class="keyword">typename</span> T::Scalar ang = omega.norm();</div><div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;  <span class="keywordflow">if</span> (ang &gt; 0) {</div><div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;    axis = omega / ang;</div><div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;  } <span class="keywordflow">else</span> {</div><div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;    axis = <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a>(1, 0, 0);</div><div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;  }</div><div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;</div><div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;  ang *= dt;</div><div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> ee = std::sin(ang / 2) * axis;</div><div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat&lt;typename T::Scalar&gt;</a> quatD(std::cos(ang / 2), ee[0], ee[1], ee[2]);</div><div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;</div><div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat&lt;typename T::Scalar&gt;</a> quatNew = <a class="code" href="../../da/d9b/namespaceori.html#a89494866325446c634184782e56113ff">quatProduct</a>(quat, quatD);</div><div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;  quatNew = quatNew / quatNew.norm();</div><div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;  <span class="keywordflow">return</span> quatNew;</div><div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_a8686862774f7c3186c7920447f4de282"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 4, 1 &gt; Quat</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00058">cppTypes.h:58</a></div></div>
<div class="ttc" id="cpp_types_8h_html_a6f07728c866b15ff0676a9b2ebfd2ba6"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 1 &gt; Vec3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00026">cppTypes.h:26</a></div></div>
<div class="ttc" id="namespaceori_html_a89494866325446c634184782e56113ff"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a89494866325446c634184782e56113ff">ori::quatProduct</a></div><div class="ttdeci">Quat&lt; typename T::Scalar &gt; quatProduct(const Eigen::MatrixBase&lt; T &gt; &amp;q1, const Eigen::MatrixBase&lt; T &gt; &amp;q2)</div><div class="ttdef"><b>Definition:</b> <a href="../../d4/dfb/orientation__tools_8h_source.html#l00262">orientation_tools.h:262</a></div></div>
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template&lt;typename T &gt; </div>
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          <td class="memname"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a>&lt;typename T::Scalar&gt; ori::matToSkewVec </td>
          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>m</em></td><td>)</td>
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<p>Put the skew-symmetric component of 3x3 matrix m into a 3x1 vector </p>

<p>Definition at line <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00108">108</a> of file <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html">orientation_tools.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;                                                                 {</div><div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;  static_assert(T::ColsAtCompileTime == 3 &amp;&amp; T::RowsAtCompileTime == 3,</div><div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;                <span class="stringliteral">&quot;Must have 3x3 matrix&quot;</span>);</div><div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;  <span class="keywordflow">return</span> 0.5 * <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a>(m(2, 1) - m(1, 2), m(0, 2) - m(2, 0),</div><div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;                                        (m(1, 0) - m(0, 1)));</div><div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_a6f07728c866b15ff0676a9b2ebfd2ba6"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 1 &gt; Vec3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00026">cppTypes.h:26</a></div></div>
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          <td class="memname"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a>&lt;typename T::Scalar&gt; ori::quatDerivative </td>
          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>q</em>, </td>
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        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T2 &gt; &amp;&#160;</td>
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          <td>)</td>
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<p>Quaternion derivative calculation, like rqd(q, omega) in MATLAB. the omega is expressed in body frame </p><dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">q</td><td></td></tr>
    <tr><td class="paramname">omega</td><td></td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd></dd></dl>

<p>Definition at line <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00240">240</a> of file <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html">orientation_tools.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;                                                                          {</div><div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;  static_assert(T::ColsAtCompileTime == 1 &amp;&amp; T::RowsAtCompileTime == 4,</div><div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;                <span class="stringliteral">&quot;Must have 4x1 quat&quot;</span>);</div><div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;  static_assert(T2::ColsAtCompileTime == 1 &amp;&amp; T2::RowsAtCompileTime == 3,</div><div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;                <span class="stringliteral">&quot;Must have 3x1 omega&quot;</span>);</div><div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;  <span class="comment">// first case in rqd</span></div><div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a5e48cf69558cf96d92f71803cf9d19a4">Mat4&lt;typename T::Scalar&gt;</a> Q;</div><div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;  Q &lt;&lt; q[0], -q[1], -q[2], -q[3], q[1], q[0], -q[3], q[2], q[2], q[3], q[0],</div><div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;      -q[1], q[3], -q[2], q[1], q[0];</div><div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;</div><div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat&lt;typename T::Scalar&gt;</a> qq(</div><div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;      <a class="code" href="../../da/d9b/namespaceori.html#a324ebc9ef2225bdf72de8d94408bf047">quaternionDerviativeStabilization</a> * omega.norm() * (1 - q.norm()),</div><div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;      omega[0], omega[1], omega[2]);</div><div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat&lt;typename T::Scalar&gt;</a> dq = 0.5 * Q * qq;</div><div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;  <span class="keywordflow">return</span> dq;</div><div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_a5e48cf69558cf96d92f71803cf9d19a4"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a5e48cf69558cf96d92f71803cf9d19a4">Mat4</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 4, 4 &gt; Mat4</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00094">cppTypes.h:94</a></div></div>
<div class="ttc" id="cpp_types_8h_html_a8686862774f7c3186c7920447f4de282"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 4, 1 &gt; Quat</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00058">cppTypes.h:58</a></div></div>
<div class="ttc" id="namespaceori_html_a324ebc9ef2225bdf72de8d94408bf047"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a324ebc9ef2225bdf72de8d94408bf047">ori::quaternionDerviativeStabilization</a></div><div class="ttdeci">static constexpr double quaternionDerviativeStabilization</div><div class="ttdef"><b>Definition:</b> <a href="../../d4/dfb/orientation__tools_8h_source.html#l00030">orientation_tools.h:30</a></div></div>
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          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
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<p>Convert a quaternion to a rotation matrix. This matrix represents a coordinate transformation into the frame which has the orientation specified by the quaternion </p>

<p>Definition at line <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00160">160</a> of file <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html">orientation_tools.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;                                 {</div><div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;  static_assert(T::ColsAtCompileTime == 1 &amp;&amp; T::RowsAtCompileTime == 4,</div><div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;                <span class="stringliteral">&quot;Must have 4x1 quat&quot;</span>);</div><div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;  <span class="keyword">typename</span> T::Scalar e0 = q(0);</div><div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;  <span class="keyword">typename</span> T::Scalar e1 = q(1);</div><div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;  <span class="keyword">typename</span> T::Scalar e2 = q(2);</div><div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;  <span class="keyword">typename</span> T::Scalar e3 = q(3);</div><div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;</div><div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3&lt;typename T::Scalar&gt;</a> R;</div><div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;</div><div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;  R &lt;&lt; 1 - 2 * (e2 * e2 + e3 * e3), 2 * (e1 * e2 - e0 * e3),</div><div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;      2 * (e1 * e3 + e0 * e2), 2 * (e1 * e2 + e0 * e3),</div><div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;      1 - 2 * (e1 * e1 + e3 * e3), 2 * (e2 * e3 - e0 * e1),</div><div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;      2 * (e1 * e3 - e0 * e2), 2 * (e2 * e3 + e0 * e1),</div><div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;      1 - 2 * (e1 * e1 + e2 * e2);</div><div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;  R.transposeInPlace();</div><div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;  <span class="keywordflow">return</span> R;</div><div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_aa8cb424e643d476ea485238dad7c3e18"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 3 &gt; Mat3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00054">cppTypes.h:54</a></div></div>
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          <td class="memname">void ori::quaternionToso3 </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a>&lt; T &gt;&#160;</td>
          <td class="paramname"><em>quat</em>, </td>
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        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a>&lt; T &gt; &amp;&#160;</td>
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        </tr>
        <tr>
          <td></td>
          <td>)</td>
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<p>Definition at line <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00340">340</a> of file <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html">orientation_tools.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;                                                       {</div><div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;  so3[0] = quat[1];</div><div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;  so3[1] = quat[2];</div><div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;  so3[2] = quat[3];</div><div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;</div><div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;  T theta =</div><div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;      2.0 * asin(sqrt(so3[0] * so3[0] + so3[1] * so3[1] + so3[2] * so3[2]));</div><div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;</div><div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;  <span class="keywordflow">if</span> (fabs(theta) &lt; 0.0000001) {</div><div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;    so3.setZero();</div><div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;    <span class="keywordflow">return</span>;</div><div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;  }</div><div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;  so3 /= sin(theta / 2.0);</div><div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;  so3 *= theta;</div><div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;}</div></div><!-- fragment -->
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          <td class="memname"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a>&lt;typename T::Scalar&gt; ori::quatProduct </td>
          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>q1</em>, </td>
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        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
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<p>Take the product of two quaternions </p>

<p>Definition at line <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00262">262</a> of file <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html">orientation_tools.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;                                                                   {</div><div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;  <span class="keyword">typename</span> T::Scalar r1 = q1[0];</div><div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;  <span class="keyword">typename</span> T::Scalar r2 = q2[0];</div><div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> v1(q1[1], q1[2], q1[3]);</div><div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> v2(q2[1], q2[2], q2[3]);</div><div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;</div><div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;  <span class="keyword">typename</span> T::Scalar r = r1 * r2 - v1.dot(v2);</div><div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> v = r1 * v2 + r2 * v1 + v1.cross(v2);</div><div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat&lt;typename T::Scalar&gt;</a> q(r, v[0], v[1], v[2]);</div><div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;  <span class="keywordflow">return</span> q;</div><div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_a8686862774f7c3186c7920447f4de282"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 4, 1 &gt; Quat</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00058">cppTypes.h:58</a></div></div>
<div class="ttc" id="cpp_types_8h_html_a6f07728c866b15ff0676a9b2ebfd2ba6"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 1 &gt; Vec3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00026">cppTypes.h:26</a></div></div>
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          <td class="memname"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a>&lt;typename T::Scalar&gt; ori::quatToRPY </td>
          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>q</em></td><td>)</td>
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<p>Convert a quaternion to RPY. Uses ZYX order (yaw-pitch-roll), but returns angles in (roll, pitch, yaw). </p>

<p>Definition at line <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00185">185</a> of file <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html">orientation_tools.h</a>.</p>

<p>References <a class="el" href="../../de/dda/_math_utilities_8h_source.html#l00015">square()</a>.</p>
<div class="fragment"><div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;                                                              {</div><div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;  static_assert(T::ColsAtCompileTime == 1 &amp;&amp; T::RowsAtCompileTime == 4,</div><div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;                <span class="stringliteral">&quot;Must have 4x1 quat&quot;</span>);</div><div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> rpy;</div><div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;  <span class="keyword">typename</span> T::Scalar as = std::min(-2. * (q[1] * q[3] - q[0] * q[2]), .99999);</div><div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;  rpy(2) =</div><div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;      std::atan2(2 * (q[1] * q[2] + q[0] * q[3]),</div><div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;                 <a class="code" href="../../de/dda/_math_utilities_8h.html#a4f88262a43b7f84fc10183a1f82f6b66">square</a>(q[0]) + <a class="code" href="../../de/dda/_math_utilities_8h.html#a4f88262a43b7f84fc10183a1f82f6b66">square</a>(q[1]) - <a class="code" href="../../de/dda/_math_utilities_8h.html#a4f88262a43b7f84fc10183a1f82f6b66">square</a>(q[2]) - <a class="code" href="../../de/dda/_math_utilities_8h.html#a4f88262a43b7f84fc10183a1f82f6b66">square</a>(q[3]));</div><div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;  rpy(1) = std::asin(as);</div><div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;  rpy(0) =</div><div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;      std::atan2(2 * (q[2] * q[3] + q[0] * q[1]),</div><div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;                 <a class="code" href="../../de/dda/_math_utilities_8h.html#a4f88262a43b7f84fc10183a1f82f6b66">square</a>(q[0]) - <a class="code" href="../../de/dda/_math_utilities_8h.html#a4f88262a43b7f84fc10183a1f82f6b66">square</a>(q[1]) - <a class="code" href="../../de/dda/_math_utilities_8h.html#a4f88262a43b7f84fc10183a1f82f6b66">square</a>(q[2]) + <a class="code" href="../../de/dda/_math_utilities_8h.html#a4f88262a43b7f84fc10183a1f82f6b66">square</a>(q[3]));</div><div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;  <span class="keywordflow">return</span> rpy;</div><div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;}</div><div class="ttc" id="_math_utilities_8h_html_a4f88262a43b7f84fc10183a1f82f6b66"><div class="ttname"><a href="../../de/dda/_math_utilities_8h.html#a4f88262a43b7f84fc10183a1f82f6b66">square</a></div><div class="ttdeci">T square(T a)</div><div class="ttdef"><b>Definition:</b> <a href="../../de/dda/_math_utilities_8h_source.html#l00015">MathUtilities.h:15</a></div></div>
<div class="ttc" id="cpp_types_8h_html_a6f07728c866b15ff0676a9b2ebfd2ba6"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 1 &gt; Vec3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00026">cppTypes.h:26</a></div></div>
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          <td class="memname"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a>&lt;typename T::Scalar&gt; ori::quatToso3 </td>
          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>q</em></td><td>)</td>
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<p>Convert a quaternion to so3. </p>

<p>Definition at line <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00213">213</a> of file <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html">orientation_tools.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;                                                              {</div><div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;  static_assert(T::ColsAtCompileTime == 1 &amp;&amp; T::RowsAtCompileTime == 4,</div><div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;                <span class="stringliteral">&quot;Must have 4x1 quat&quot;</span>);</div><div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> so3;</div><div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;  <span class="keyword">typename</span> T::Scalar theta = 2. * std::acos(q[0]);</div><div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;  so3[0] = theta * q[1] / std::sin(theta / 2.);</div><div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;  so3[1] = theta * q[2] / std::sin(theta / 2.);</div><div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;  so3[2] = theta * q[3] / std::sin(theta / 2.);</div><div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;  <span class="keywordflow">return</span> so3;</div><div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_a6f07728c866b15ff0676a9b2ebfd2ba6"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 1 &gt; Vec3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00026">cppTypes.h:26</a></div></div>
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          <td class="memname">T ori::rad2deg </td>
          <td>(</td>
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<p>Convert radians to degrees </p>

<p>Definition at line <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00038">38</a> of file <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html">orientation_tools.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;                 {</div><div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;  static_assert(std::is_floating_point&lt;T&gt;::value,</div><div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;                <span class="stringliteral">&quot;must use floating point value&quot;</span>);</div><div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;  <span class="keywordflow">return</span> rad * T(180) / T(M_PI);</div><div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;}</div></div><!-- fragment -->
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          <td class="memname"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a>&lt;typename T::Scalar&gt; ori::rotationMatrixToQuaternion </td>
          <td>(</td>
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<p>Convert a coordinate transformation matrix to an orientation quaternion. </p>

<p>Definition at line <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00119">119</a> of file <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html">orientation_tools.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;                                  {</div><div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;  static_assert(T::ColsAtCompileTime == 3 &amp;&amp; T::RowsAtCompileTime == 3,</div><div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;                <span class="stringliteral">&quot;Must have 3x3 matrix&quot;</span>);</div><div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat&lt;typename T::Scalar&gt;</a> q;</div><div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3&lt;typename T::Scalar&gt;</a> r = r1.transpose();</div><div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;  <span class="keyword">typename</span> T::Scalar tr = r.trace();</div><div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;  <span class="keywordflow">if</span> (tr &gt; 0.0) {</div><div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;    <span class="keyword">typename</span> T::Scalar S = sqrt(tr + 1.0) * 2.0;</div><div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;    q(0) = 0.25 * S;</div><div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;    q(1) = (r(2, 1) - r(1, 2)) / S;</div><div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;    q(2) = (r(0, 2) - r(2, 0)) / S;</div><div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;    q(3) = (r(1, 0) - r(0, 1)) / S;</div><div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> ((r(0, 0) &gt; r(1, 1)) &amp;&amp; (r(0, 0) &gt; r(2, 2))) {</div><div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;    <span class="keyword">typename</span> T::Scalar S = sqrt(1.0 + r(0, 0) - r(1, 1) - r(2, 2)) * 2.0;</div><div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;    q(0) = (r(2, 1) - r(1, 2)) / S;</div><div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;    q(1) = 0.25 * S;</div><div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;    q(2) = (r(0, 1) + r(1, 0)) / S;</div><div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;    q(3) = (r(0, 2) + r(2, 0)) / S;</div><div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (r(1, 1) &gt; r(2, 2)) {</div><div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;    <span class="keyword">typename</span> T::Scalar S = sqrt(1.0 + r(1, 1) - r(0, 0) - r(2, 2)) * 2.0;</div><div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;    q(0) = (r(0, 2) - r(2, 0)) / S;</div><div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;    q(1) = (r(0, 1) + r(1, 0)) / S;</div><div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;    q(2) = 0.25 * S;</div><div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;    q(3) = (r(1, 2) + r(2, 1)) / S;</div><div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;  } <span class="keywordflow">else</span> {</div><div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;    <span class="keyword">typename</span> T::Scalar S = sqrt(1.0 + r(2, 2) - r(0, 0) - r(1, 1)) * 2.0;</div><div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;    q(0) = (r(1, 0) - r(0, 1)) / S;</div><div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;    q(1) = (r(0, 2) + r(2, 0)) / S;</div><div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;    q(2) = (r(1, 2) + r(2, 1)) / S;</div><div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;    q(3) = 0.25 * S;</div><div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;  }</div><div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;  <span class="keywordflow">return</span> q;</div><div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_aa8cb424e643d476ea485238dad7c3e18"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 3 &gt; Mat3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00054">cppTypes.h:54</a></div></div>
<div class="ttc" id="cpp_types_8h_html_a8686862774f7c3186c7920447f4de282"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 4, 1 &gt; Quat</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00058">cppTypes.h:58</a></div></div>
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          <td class="memname"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a>&lt;typename T::Scalar&gt; ori::rotationMatrixToRPY </td>
          <td>(</td>
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<p>Definition at line <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00225">225</a> of file <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html">orientation_tools.h</a>.</p>

<p>References <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00185">quatToRPY()</a>, and <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00119">rotationMatrixToQuaternion()</a>.</p>
<div class="fragment"><div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;                                                                        {</div><div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;  static_assert(T::ColsAtCompileTime == 3 &amp;&amp; T::RowsAtCompileTime == 3,</div><div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;                <span class="stringliteral">&quot;Must have 3x3 matrix&quot;</span>);</div><div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat&lt;typename T::Scalar&gt;</a> q = <a class="code" href="../../da/d9b/namespaceori.html#a73c3872af6870d856cedd662856fcaea">rotationMatrixToQuaternion</a>(R);</div><div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> rpy = <a class="code" href="../../da/d9b/namespaceori.html#add76bed815809cbebd38a8596b0f6224">quatToRPY</a>(q);</div><div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;  <span class="keywordflow">return</span> rpy;</div><div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_a8686862774f7c3186c7920447f4de282"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 4, 1 &gt; Quat</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00058">cppTypes.h:58</a></div></div>
<div class="ttc" id="cpp_types_8h_html_a6f07728c866b15ff0676a9b2ebfd2ba6"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 1 &gt; Vec3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00026">cppTypes.h:26</a></div></div>
<div class="ttc" id="namespaceori_html_add76bed815809cbebd38a8596b0f6224"><div class="ttname"><a href="../../da/d9b/namespaceori.html#add76bed815809cbebd38a8596b0f6224">ori::quatToRPY</a></div><div class="ttdeci">Vec3&lt; typename T::Scalar &gt; quatToRPY(const Eigen::MatrixBase&lt; T &gt; &amp;q)</div><div class="ttdef"><b>Definition:</b> <a href="../../d4/dfb/orientation__tools_8h_source.html#l00185">orientation_tools.h:185</a></div></div>
<div class="ttc" id="namespaceori_html_a73c3872af6870d856cedd662856fcaea"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a73c3872af6870d856cedd662856fcaea">ori::rotationMatrixToQuaternion</a></div><div class="ttdeci">Quat&lt; typename T::Scalar &gt; rotationMatrixToQuaternion(const Eigen::MatrixBase&lt; T &gt; &amp;r1)</div><div class="ttdef"><b>Definition:</b> <a href="../../d4/dfb/orientation__tools_8h_source.html#l00119">orientation_tools.h:119</a></div></div>
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          <td class="memname"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a>&lt;typename T::Scalar&gt; ori::rpyToQuat </td>
          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>rpy</em></td><td>)</td>
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<p>Definition at line <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00201">201</a> of file <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html">orientation_tools.h</a>.</p>

<p>References <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00119">rotationMatrixToQuaternion()</a>, and <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00083">rpyToRotMat()</a>.</p>
<div class="fragment"><div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;                                                                {</div><div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;  static_assert(T::ColsAtCompileTime == 1 &amp;&amp; T::RowsAtCompileTime == 3,</div><div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;                <span class="stringliteral">&quot;Must have 3x1 vec&quot;</span>);</div><div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3&lt;typename T::Scalar&gt;</a> R = <a class="code" href="../../da/d9b/namespaceori.html#add867f41c8046a8bba05611e25c8dfcd">rpyToRotMat</a>(rpy);</div><div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat&lt;typename T::Scalar&gt;</a> q = <a class="code" href="../../da/d9b/namespaceori.html#a73c3872af6870d856cedd662856fcaea">rotationMatrixToQuaternion</a>(R);</div><div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;  <span class="keywordflow">return</span> q;</div><div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;}</div><div class="ttc" id="namespaceori_html_add867f41c8046a8bba05611e25c8dfcd"><div class="ttname"><a href="../../da/d9b/namespaceori.html#add867f41c8046a8bba05611e25c8dfcd">ori::rpyToRotMat</a></div><div class="ttdeci">Mat3&lt; typename T::Scalar &gt; rpyToRotMat(const Eigen::MatrixBase&lt; T &gt; &amp;v)</div><div class="ttdef"><b>Definition:</b> <a href="../../d4/dfb/orientation__tools_8h_source.html#l00083">orientation_tools.h:83</a></div></div>
<div class="ttc" id="cpp_types_8h_html_aa8cb424e643d476ea485238dad7c3e18"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 3 &gt; Mat3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00054">cppTypes.h:54</a></div></div>
<div class="ttc" id="cpp_types_8h_html_a8686862774f7c3186c7920447f4de282"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 4, 1 &gt; Quat</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00058">cppTypes.h:58</a></div></div>
<div class="ttc" id="namespaceori_html_a73c3872af6870d856cedd662856fcaea"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a73c3872af6870d856cedd662856fcaea">ori::rotationMatrixToQuaternion</a></div><div class="ttdeci">Quat&lt; typename T::Scalar &gt; rotationMatrixToQuaternion(const Eigen::MatrixBase&lt; T &gt; &amp;r1)</div><div class="ttdef"><b>Definition:</b> <a href="../../d4/dfb/orientation__tools_8h_source.html#l00119">orientation_tools.h:119</a></div></div>
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          <td class="memname"><a class="el" href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3</a>&lt;typename T::Scalar&gt; ori::rpyToRotMat </td>
          <td>(</td>
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<p>Go from rpy to rotation matrix. </p>

<p>Definition at line <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00083">83</a> of file <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html">orientation_tools.h</a>.</p>

<p>References <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00060">coordinateRotation()</a>, <a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>, <a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a57cec4137b614c87cb4e24a3d003a3e0">Y</a>, and <a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a21c2e59531c8710156d34a3c30ac81d5">Z</a>.</p>
<div class="fragment"><div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;                                                                {</div><div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;  static_assert(T::ColsAtCompileTime == 1 &amp;&amp; T::RowsAtCompileTime == 3,</div><div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;                <span class="stringliteral">&quot;must have 3x1 vector&quot;</span>);</div><div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3&lt;typename T::Scalar&gt;</a> m = <a class="code" href="../../da/d9b/namespaceori.html#a537b8d0769c03e4cd8ef2b9a9dc8a760">coordinateRotation</a>(CoordinateAxis::X, v[0]) *</div><div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;                               <a class="code" href="../../da/d9b/namespaceori.html#a537b8d0769c03e4cd8ef2b9a9dc8a760">coordinateRotation</a>(CoordinateAxis::Y, v[1]) *</div><div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;                               <a class="code" href="../../da/d9b/namespaceori.html#a537b8d0769c03e4cd8ef2b9a9dc8a760">coordinateRotation</a>(CoordinateAxis::Z, v[2]);</div><div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;  <span class="keywordflow">return</span> m;</div><div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;}</div><div class="ttc" id="namespaceori_html_a537b8d0769c03e4cd8ef2b9a9dc8a760"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a537b8d0769c03e4cd8ef2b9a9dc8a760">ori::coordinateRotation</a></div><div class="ttdeci">Mat3&lt; T &gt; coordinateRotation(CoordinateAxis axis, T theta)</div><div class="ttdef"><b>Definition:</b> <a href="../../d4/dfb/orientation__tools_8h_source.html#l00060">orientation_tools.h:60</a></div></div>
<div class="ttc" id="cpp_types_8h_html_aa8cb424e643d476ea485238dad7c3e18"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 3 &gt; Mat3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00054">cppTypes.h:54</a></div></div>
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          <td class="memname"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a>&lt;T&gt; ori::so3ToQuat </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a>&lt; T &gt; &amp;&#160;</td>
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<p>Definition at line <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00356">356</a> of file <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html">orientation_tools.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;                                {</div><div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat&lt;T&gt;</a> quat;</div><div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;</div><div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;  T theta = sqrt(so3[0] * so3[0] + so3[1] * so3[1] + so3[2] * so3[2]);</div><div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;</div><div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;  <span class="keywordflow">if</span> (fabs(theta) &lt; 1.e-6) {</div><div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;    quat.setZero();</div><div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;    quat[0] = 1.;</div><div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;    <span class="keywordflow">return</span> quat;</div><div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;  }</div><div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;  quat[0] = cos(theta / 2.);</div><div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;  quat[1] = so3[0] / theta * sin(theta / 2.);</div><div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;  quat[2] = so3[1] / theta * sin(theta / 2.);</div><div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;  quat[3] = so3[2] / theta * sin(theta / 2.);</div><div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;  <span class="keywordflow">return</span> quat;</div><div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_a8686862774f7c3186c7920447f4de282"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a8686862774f7c3186c7920447f4de282">Quat</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 4, 1 &gt; Quat</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00058">cppTypes.h:58</a></div></div>
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          <td class="memname"><a class="el" href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3</a>&lt;typename T::Scalar&gt; ori::vectorToSkewMat </td>
          <td>(</td>
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<p>Convert a 3x1 vector to a skew-symmetric 3x3 matrix </p>

<p>Definition at line <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00096">96</a> of file <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html">orientation_tools.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;                                                                    {</div><div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;  static_assert(T::ColsAtCompileTime == 1 &amp;&amp; T::RowsAtCompileTime == 3,</div><div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;                <span class="stringliteral">&quot;Must have 3x1 matrix&quot;</span>);</div><div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3&lt;typename T::Scalar&gt;</a> m;</div><div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;  m &lt;&lt; 0, -v[2], v[1], v[2], 0, -v[0], -v[1], v[0], 0;</div><div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;  <span class="keywordflow">return</span> m;</div><div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_aa8cb424e643d476ea485238dad7c3e18"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 3 &gt; Mat3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00054">cppTypes.h:54</a></div></div>
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<h2 class="groupheader">Variable Documentation</h2>
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          <td class="memname">constexpr double ori::quaternionDerviativeStabilization = 0.1</td>
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<p>Definition at line <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00030">30</a> of file <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html">orientation_tools.h</a>.</p>

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